A Cultural Paradox Fun in Mathematics by Jeffrey A. Zilahy - HTML preview

CH 17: One Heck of a Ratio

π , or Pi, is known by most people as being 3.14. It is also known as the ratio of the circumference of a circle to its diameter. Put another way; consider that every circle, regardless of its size, has a little over three times the distance around the circle compared to a line that bisects the circle into two halves. While this might seem like a rather esoteric mathematical tidbit, it has profound implications and a storied history. For starters, π is likely the most well known ratio ever known by humanity. π is known as a transcendental number which means that we know for a fact (we call such facts mathematical proofs) that the decimal expansion of π is non– terminating and non-repeating. These digits will never end and there is no pattern. We also know that π is an irrational number. This means it is impossible to ever find any two integers that are a ratio of π .

Today, with the power of computers we know more than trillions of digits of π and in fact, memorizing digits of π is a bit of a geek phenomenon, the record is currently held by Akira Haraguchi who managed to memorize 100,000 digits of π . To put that in perspective, imagine trying to memorize a book hundreds of pages long of random numbers.